John Krafcik, CEO of the company's American unit, said fuel-efficiency and mpg ratings will continue to be a focal point of Hyundai marketing, even as its trust with many buyers has been dented. Hyundai and sister brand Kia are adjusting the ratings of 900,000 vehicles sold in the 2011-2013 model years. It affects more than one-third of all Hyundai and Kia vehicles sold during that time. Hyundai overstated fuel-economy figures by an average of 3 percent.

Krafcik said Hyundai has sent letters to consumers and will reimburse them for as long as they own their vehicles.

"We're treating this like the serious matter that it is," he said in remarks at the Los Angeles Auto Show. "This whole episode has been a difficult one for Hyundai."

About 90 percent of customers have been satisfied with Hyundai's steps, Krafcik said.

Still, he wouldn't discuss legal implications for the company and wouldn't specify figures for any potential settlements.

"I don't know what the number is going to be," he said.

He also wouldn't speak to any disciplinary actions for company officials, saying "that's not for me to decide."

After aggressively touting its lineup of vehicles hitting at least 40 mpg, Krafcik said the company no longer has any that officially reach that mark. Despite this, fuel efficiency will remain a highlight of marketing efforts.

"It's been a cornerstone of our brand, and we're going to continue," he said.

Though the brand's reputation has taken a hit, Hyundai has added another shift at its Alabama factory to meet demand and is still within reach of a record sales year. The added shift will mean an extra 15,000 vehicles this year and 60,000 annually over a full year.

In other comments, Krafcik said Hyundai will consider making a special model or option such as the Veloster C3 concept revealed at the show. It has a canvas roof that rolls back to completely open the rear of the car. The concept also has side skirts, 18-inch wheels, and a bicycling and skateboard theme.